Preheat oven to 350 degrees. For the cake, combine cake mix, margarine, 1/2 cup juice from the mandarin oranges, eggs, and vanilla. Beat for four minutes on medium-high. Add drained oranges and beat again until pieces are broken up and small. Pour batter into greased and floured 9 x 13 inch baking pan and bake for 25 to 30 minutes, or until golden brown and set. Remove from oven and cool completely. If desired, turn out cake onto a large platter.
Once cake is cool, blend juice from drained pineapples with the vanilla pudding mix. Add powdered sugar and mix, then mix in whipped topping. Stir in drained pineapple. Spread on cooled cake and refrigerate several hours.
To serve, cut cake into squares and top each square with a mandarin orange slice.